Copy a node-based material to another object, and then freely edit the second one?
This probably has already been solved by the OP, but I came across this problem myself and searching for an answer I stumbled upon this post.

And for the sake of those eventually looking to solve the same problem, I'd like to add an important detail:

The answer given by Duarte Farrajota Ramos is correct, yet the OP said he was still having trouble, and in fact so did I after following his instructions (in fact I was already doing all that he said even before seeing his answer, and it wasn't working), the problem here is the nested/grouped nodes inside the material, they have defined users as well, and if you just make the main material (in the material tab) single-user, the alterations you make on the first level of nodes in fact won't be passed on to the original materials, but if you alter the inner layers, I mean, alter things inside the groups that compose the material, it WILL change the original material you used as a base. Note, this will happen even if you create a material from scratch and copy/paste the nodes from another material, cause the data of the inner groups is still being shared between materials, only the outer layer is in "single user mode".

To solve this, you must simply create the new material, make it single user on the material tab by clicking it's users number (if there is any), this will make the outer node layer single user. Then go in node edit mode, look for the grouped nodes and do the same, you'll see they have their own users number, click on that, and now you can alter whatever you want, and nothing will get out of that material.

Material tab, you can see there are no users, yet I was still getting my base material changed:



Node editor, and here I found the problem, the inner node group was being shared with other 8 materials:



This is indeed some really basic stuff, but for newcomers it might prove to be a challenge, cause it may just pass unnoticed that you must clear the users from all layers. Hope I can help someone. Cheers!